We solve the initial value problem for the diffusion induced by dyadic fractional derivative s in \mathbb{R}^{+}. First we obtain the spectral analysis of the dyadic fractional derivative operator in terms of the Haar system, which unveils a structure for the underlying “heat kernel”. We show that this kernel admits an integrable and decreasing majorant that involves the dyadic distance. This allows us to provide an estimate of the maximal operator of the diffusion by the Hardy-Littlewood dyadic maximal operator. As a consequence we obtain the pointwise convergence to the initial data., Marcelo Actis, Hugo Aimar., and Obsahuje seznam literatury
Given a distribution $T$ on the sphere we define, in analogy to the work of Łojasiewicz, the value of $T$ at a point $\xi$ of the sphere and we show that if $T$ has the value $\tau$ at $\xi$, then the Fourier-Laplace series of $T$ at $\xi$ is Abel-summable to $\tau$., Francisco Javier González Vieli., and Obsahuje bibliografii
In this paper, we study the structure of polycyclic groups admitting an automorphism of order four on the basis of Neumann’s result, and prove that if α is an automorphism of order four of a polycyclic group G and the map φ: G → G defined by gφ = [g,α] is surjective, then G contains a characteristic subgroup H of finite index such that the second derived subgroup H″ is included in the centre of H and CH(α2) is abelian, both CG(α2) and G/[G, α2] are abelian-by-finite. These results extend recent and classical results in the literature., Tao Xu, Fang Zhou, Heguo Liu., and Obsahuje seznam literatury
We describe the relation between quasi-minuscule representations, polytopes and Weyl group orbits in Picard lattices of rational surfaces. As an application, to each quasi-minuscule representation we attach a class of rational surfaces, and realize such a representation as an associated vector bundle of a principal bundle over these surfaces. Moreover, any quasi-minuscule representation can be defined by rational curves, or their disjoint unions in a rational surface, satisfying certain natural numerical conditions., Jae-Hyouk Lee, Mang Xu, Jiajin Zhang., and Seznam literatury
We consider a single-species stochastic logistic model with the population's nonlinear diffusion between two patches. We prove the system is stochastically permanent and persistent in mean, and then we obtain sufficient conditions for stationary distribution and extinction. Finally, we illustrate our conclusions through numerical simulation., Li Zu, Daqing Jiang, Donal O'Regan., and Obsahuje bibliografii